Abstract
We compute the vacuum polarization for a massless, conformally coupled scalar field on the covering space of global, four-dimensional, anti-de Sitter space-time. Since anti-de Sitter space is not globally hyperbolic, boundary conditions must be applied to the scalar field. We consider general Robin (mixed) boundary conditions for which the classical evolution of the field is well-defined and stable. The vacuum expectation value of the square of the field is not constant unless either Dirichlet or Neumann boundary conditions are applied. We also compute the thermal expectation value of the square of the field. For Dirichlet boundary conditions, both thermal and vacuum expectation values approach the same well-known limit on the space-time boundary. For all other Robin boundary conditions (including Neumann boundary conditions), the vacuum and thermal expectation values have the same limit on the space-time boundary, but this limit does not equal that in the Dirichlet case.
Highlights
Quantum field theory (QFT) on anti-de Sitter (AdS) space-time has been the subject of considerable attention owing to its role in the holographic principle and string theory, within the context of the AdS/CFT correspondence
We develop a methodology which enables the efficient computation of this quantity for Robin boundary conditions, and employ this to present novel results for the vacuum polarization for conformal scalar fields for which all modes satisfy general Robin boundary conditions
This paper has been concerned with the renormalized vacuum polarization for a massless, conformally coupled scalar field on the global four-dimensional AdS
Summary
Quantum field theory (QFT) on anti-de Sitter (AdS) space-time has been the subject of considerable attention owing to its role in the holographic principle and string theory, within the context of the AdS/CFT (conformal field theory) correspondence (see for example [1] for a review). We focus on the role the boundary conditions play for both vacuum and thermal states of a massless, conformally coupled scalar field on the covering space of global AdS in four space-time dimensions. The study of (d, e) has been initiated with a computation of the renormalized vacuum polarization and stress–energy tensor for a massless, conformally coupled scalar field for which most of the field modes satisfy Dirichlet boundary conditions, but the s-wave modes satisfy Robin boundary conditions [6]. We derive a mode-sum expression for the Wightman function for the vacuum state, with Robin boundary conditions applied consistently to all field modes This expression does not lend itself to a practical method of computing renormalized expectation values, so in section 4 we consider the related problem of constructing thermal states on the Euclidean section of AdS.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
